What is the value of tan(arcsin((-1)/2)) ?

The value of tan(arcsin((-1)/2)) is -(sqrt(3))/3

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tan(arcsin((-1)/2))

tan (arcsin (\frac{- 1}{2}))

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

tan (arcsin (\frac{- 1}{2}))

Rewrite using trig identities:

tan (arcsin (\frac{- 1}{2})) = \frac{( \frac{- 1}{2} ) 1 - ( \frac{- 1}{2} ) ^{2}}{1 - ( \frac{- 1}{2} ) ^{2}}

Use the following identity:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

= \frac{( \frac{- 1}{2} ) 1 - ( \frac{- 1}{2} ) ^{2}}{1 - ( \frac{- 1}{2} ) ^{2}}

= \frac{\frac{- 1}{2} 1 - ( \frac{- 1}{2} ) ^{2}}{1 - ( \frac{- 1}{2} ) ^{2}}

Simplify

= - \frac{3}{3}

csc (7 0^{\circ})

2 cos^{2} (157. 5^{\circ}) - 1

sin (\frac{2 π}{7})

cos (- \frac{11 π}{3})

- sin (\frac{4 π}{3})

What is the value of tan(arcsin((-1)/2)) ?
The value of tan(arcsin((-1)/2)) is -(sqrt(3))/3